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arXiv · 0708.1347

Quantized Non-Abelian Monopoles on S^3

Irit Maor·Harsh Mathur·Tanmay Vachaspati
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Abstract

A possible electric-magnetic duality suggests that the confinement of non-Abelian electric charges manifests itself as a perturbative quantum effect for the dual magnetic charges. Motivated by this possibility, we study vacuum fluctuations around a non-Abelian monopole-antimonopole pair treated as point objects with charges g=\pm n/2 (n=1,2,...), and placed on the antipodes of a three sphere of radius R. We explicitly find all the fluctuation modes by linearizing and solving the Yang-Mills equations about this background field on a three sphere. We recover, generalize and extend earlier results, including those on the stability analysis of non-Abelian magnetic monopoles. We find that for g \ge 1 monopoles there is an unstable mode that tends to squeeze magnetic flux in the angular directions. We sum the vacuum energy contributions of the fluctuation modes for the g=1/2 case and find oscillatory dependence on the cutoff scale. Subject to certain assumptions, we find that the contribution of the fluctuation modes to the quantum zero point energy behaves as -R^{-2/3} and hence decays more slowly than the classical -R^{-1} Coulomb potential for large R. However, this correction to the zero point energy does not agree with the linear growth expected if the monopoles are confined.

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Irit Maor, Harsh Mathur, Tanmay Vachaspati. 2007-08-20. Quantized Non-Abelian Monopoles on S^3. https://doi.org/10.1103/physrevd.76.105013

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